The geometry and electronic structure of self-assembled atomic scale Au wires on Si(775) are investigated within density functional theory. The calculated surface diagram indicates the existence of two stable configurations with Au coverages of 0.32 and 0.96 monolayers, respectively. The low-coverage structure is predicted to host an antiferromagnetic spin chain localized at the Si rest atom dangling bonds, while the high-coverage structure is characterized by a Au-induced β-√ 3-like structure on the terrace. These structural models are supported by the comparison of measured and calculated surface optical anisotropies.